However, the “Elements” also includes a series of theorems on the properties of numbers and integers, marking the first real beginnings of number theory. For example, Euclid proved what has become known as the Fundamental Theorem of Arithmethic (or the Unique Factorization Theorem), that every positive integer greater than 1 can be written as a product of prime numbers (or is itself a prime number). Thus, for example: 21 = 3 x 7; 113 = 1 x 113; 1,200 = 2 x 2 x 2 x 2 x 3 x 5 x 5; 6,936 = 2 x 2 x 2 x 3 x 17 x 17; etc. His proof was the first known example of a proof by contradiction (where any counter-example, which would otherwise prove an idea false, is shown to makes no logical sense itself).
Posted on: Tue, 16 Sep 2014 22:23:21 +0000
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